I now have a tank with lots of plants in it. Yay!
I ended up sort of mineralising the soil: I let it soak overnight, then manually squeezed it in handfuls & spread it out to dry in our living room. However, it took so long to dry that I only had time to soak it a second time & use it wet in the aquarium.

My assistants are included only to give an indication of size.
As I didn't want the bottom to be flat, I went and got a bunch of rock slates from the local hardware store that I piled into hills. I have no idea how badly erosion will wash things down, but I guess we'll see.

The hill on the right has only partly been covered in gravel at this stage. Using these irregular pieces was rather fun, kind of a pity they'll all (hopefully) stay hidden. The tacky background came with the tank, we'll be replacing it with something better once we figure out what we want.

The soil I lay on wet; estimating the depth was a bity tricky, but based on the volume of the two bucketfuls I used, on average there's now 2cm of soil. Sand was similar (also wet, as it's the old sand from the aquarium), but there's maybe 3cm of it on average.
The sand also, it seems, comes pre-populated with Malayan trumpet snails.

And now I have perhaps a dozen different types of plants planted. About half are previous tenants, the rest from a local shop. I'll have to look them up eventually, for now I'll wait and see if they survive. I filled the tank first to the top of the hills, planted everything, then took out the dirty water before filling it up.
Since that last photo, I've set up the external filter (Eheim Professional II) and a heater. I tried also adding one of the internal filters for some added flow, but that seemed too much so I took it out. The water's cleared up significantly since then, I'll think about another water change tomorrow if it looks necessary.